If $23=x^4+\frac{1}{x^4}$, then what is the value of $x^2+\frac{1}{x^2}$?

Step-by-step explanation:

is given.

We want to find .

If we square the value we want to find, we should wind up with some terms of the left hand side of the given.

Expand:

(We used the identity: for expansion).

Simplify this value:

We are given that the sum of the first two terms is 23.

This means .

Let's simplify the right hand side.

Now to find the value we want we must simply take the square root of both sides.

Simplify the right hand side:

Since is positive for any real value (that is not zero), then we can conclude .

36

step-by-step explanation:

step-by-step explanation:

mean or average is 40.6